Notes on Sraffa's Production, Chapter 3

Ch. 3. Proportions of Labor to Means of Production

CAUTION: This entire section appears to be completely abstract reasoning, without manipulating a model at hand. Proceed very slowly!

I found it useful to construct toy economies for my own benefit...which helps me understand the point Sraffa makes in each section.

13. Wages as a Proportion of National Income

• We now give the wage w successive values ranging from 1 to 0: these represent fractions of the national income (compare §10 and §12).
• Objective: determine how changes in the wage affects the rate of profits, and the prices of individual commodities...assuming the methods of production remain unchanged.

14. Values when whole National Income goes to Wages

• When we make w = 1, the whole national income goes to wages and r is eliminated.
• We thus revert to the systems of equations we began with (in ch. 1)! The difference being the quantities of labor are now shown explicitly instead of being represented by quantities of necessaries for subsistence.
• The relative values of commodities are in proportion to their labor cost, i.e. the quantity of labor which directly and indirectly gone to produce them. (See Sraffa's Appendix "On Sub-Systems")
• Sraffa asserts "at no other wage-level do values follow a simple rule".
  • Question: This is fairly cryptic. Does he mean values will not be in proportion to the quantity of labor which directly and indirectly produce the commodities? Or does he mean something else?
  • Answer: What Sraffa means, I believe, is that at no other wage level do we recover the first sort of model we discussed...instead we recover a system where the "relative values of commodities" are not in direct proportion to their labor costs.
  • Remark. It seems this proposition has some bearing on the labor theory of value, although not in the "obvious way"...

15. Variety in the proportions of labor to Means of Production

• Consider the situation when the wages are reduced (i.e., we don't allocate the national product as wage): a rate of profits will emerge.
• How do relative prices react to changes in wage? The key lies in the inequality of the proportions in which labor and the means of production are used in the various industries.
  • Remark. This phrasing seems ambiguous to me. What exactly is the "proportion" Sraffa speaks of? Isn't it apples and oranges? Or does he mean the ratio of "the value of the means of production" to the wage?
    
    It seems, based on reading further text, Sraffa refers to the ratio of the "value of the means of production" to the wage...well, I think he means wage (or else it could be the "value of the labor").
    
    Sraffa is motivating his "Standard commodity" (the subject of the next chapter!). The ratio, for the moment, is of values...but later we will see it doesn't matter if we use values or actual commodities. Yes it is "apples and oranges", but Sraffa's genius works this out!
• If the proportion were the same in all industries, no price-changes could ensue regardless of any diversity of the commodity-composition of the means of production in different industries.
• For in each industry, an equal deduction from the wage would yield just as much as required for paying profits on its means of production at a uniform rate without disturbing existing prices.
  • In these "proportions", the means of production must be measured by their values. But since values may change with a change in the wage, the question emerges: which values?
  • As far as establishing the equality or inequality of the proportions (that's all we're concerned with at the moment)...The answer is: all possible sets of values give the same result.
  • In effect, as we have seen, if the proportions of all the industries are equal, then values (and therefore proportions) do not change with the wage.
  • From this it follows if the proportions are unequal at the set of values corresponding to one wage, they cannot be equal at any other, and so they are unequal at all values.

16. "Deficit-Industries" and "Surplus-Industries"

• For the same reason, it is impossible for prices to remain unchanged when there is inequality of "proportions".
• Suppose prices did remain unchanged when the wage was reduced and a rate of profits emerged.
  • Since in any one industry what was saved through the wage-reduction would depend on the number of men employed — while what was necessary for paying profits at a uniform rate would depend on the aggregate value of the means of production used — industries with a sufficiently low proportion of labor to means of production would have a deficit...while industries with a sufficiently high proportion would have a surplus, on their payments for wages and profits.
  • Nothing is assumed at the moment as to what rate of profits correspond to what wage reduction. All we require at this stage is there should be a uniform wage and a uniform rate of profits throughout the system.

17. A Watershed Proportion

• There would be a "critical proportion" of labor to means of production which marked the watershed between "deficit" and "surplus" industries.
• An industry with such a proportion would show an even balance—the proceeds of the wage-reduction would provide exactly what was required for the payment of profits at the general rate.
• Whatever the precise value of that "proportion" in any system, it can be said a priori that—in a system with two or more basic industries—the industry with the lowest proportion of labor to means of production would be a "deficit" industry and the one with the highest proportion would be a "surplus" industry.

18. Price-Changes to Redress Balance

• Thus with a wage-reduction, price-changes would necessary to redress the balance in each of the "deficit" and "surplus" industries.
• We expect the price-ratio between each product and its means of production "to come into play".
  • Consider the "deficit" industry when wage is reduced. A rise in the price of the produce relatively to the means of production would help to eliminate the deficit, since it would release some of that share of the gross product into the industry which had been going to pay for the replacement of the (now cheapened) means of production.

    This would be added to the quantity available for the distribution as wages or profits.

    The price rise by itself would thus result in an increase in the magnitude (and "not merely in the value") of that part of the product of the industry which is available for distribution, despite the methods of production remaining unchanged.

• A further effect of the rise in the price of the product (relative to the means of production) would be to help a given quantity of product to go a "longer way" towards achieving the required rate of profit.
• Independent of this, the steeper the rise in the product's price relative to labor, the smaller the quantity of it absorbed by the wage.
• Conversely, price-movements in the opposite direction would accomplish the disposal of the surplus which otherwise would appear in an industry using a high "proportion" of labor to the means of production.

19. Price-Ratios of Product ot Means of Production

• It does not follow that the price of the product of an industry having a low proportion of labor to means of production (and hence a "potential deficit") would necessarily rise, with a wage-reduction, relative to its own means of production.

  "On the contrary," Sraffa writes, "it might possibly fall." The reason for this seeming contradiction: the means of production for an industry are themselves the product of one or more industries which (in turn) may employ a still lower proportion of labor to the means of production (and the same may be said for these commodities' means of production, etc.)

  In this case, the price of the product — although produced by a "deficit" industry — might fall in terms of its means of production. Its deficiency would have to be made good through a particularly steep rise relative to labor.

• Result: as wages fall, the price of the product for a low-proportion ("deficit") industry may rise or fall, or even alternate in rising and falling, relative to its means of production...while the price of the product of a high-proportion ("surplus") industry may fall or rise, or alternate. What neither can do, as we will see in §§21--22, is remain stable in price relative to its means of production throughout any range (long or short) of the wage-variation.

20. Price-Ratios between Products

• These considerations dominate the price-relation of a product to its means of production and equally to its relations to any other product.
• It's the "proportions" of labor to means of production which determines the relative "price" between commodities. NB: this is iterative, so those means of production used up are subject to the same method determining its "relative price".
• The net result and justification for price-variations from a change in distribution remains a simple one: redressing the balance in each industry.

21. A Recurrent Proportion

• We can now revert to the "critical proportion" (mentioned in §17) as the border between "deficit" industries and "surplus" ones.
• Assumption. Suppose we had an industry sector with that "critical proportion" of means of production to labor, and moreover each sector (producing each commodity used as a means of production) are themselves in this "critical proportion" state...and all the sectors involved in producing the means of production used in the production of the means of production are in that critical state, and so on.
• The commodity produced in such a sector would have its value not be affected when wages rose or fell. This can only happen from a potential deficit or surplus...but we assumed the industry was "in balance"!
  • NB: A commodity of this sort would not change its value relative to other commodities.
• Two separate conditions have been assumed to attain this result:
  1. The "balancing" proportion is used", and
  2. one and the same proportion recurs in all successive layers of the industry's aggregate means of production without limit.
• Note the second condition implies the first. This is the subject of the next section...

22. Balancing Ratio and Maximum Rate of Profits

• It will be convenient to replace the "proportion" (quantity of labor to means of production) with one of the corresponding "pure" ratios between homogeneous quantities.

  There are two such ratios:

  1. the quantity-ratio of direct to indirect labor employed; and
  2. the value-ratio of net product to means of production.

  These two ratios coincide when the value-ratio is calculated at the values for w = 1.

  Sraffa uses the latter ratio here.

• The rate of profits is uniform in all industries (and depends only on the wage), the value-ratio of the net product to the means of production is in general different for each industry and mainly depends on its particular circumstances of production.
• Exception: When we make the wage zero (i.e., w = 0) and the whole net product goes to profits, in each industry the value-ratio of the net product to means of production necessarily comes to coincide with the general rate of profits r. At this level the "value ratios" of all industries are equal, regardless of how different the "value ratios" may have been at other wage-levels.
• The only "value-ratio" which can be invariant to changes in wage (and thus capable of being "recurrent" in the sense defined in §21) is the one that is equal to the rate of profits corresponding with zero wage. And that is the "balancing" ratio.
• Definition. The Maximum Rate of Profits is the rate of profits as it would be if the whole national income went to profits, and we denote it by R.